Low density parity check encoder having length of 16200 and code rate of 3/15, and low density parity check encoding method using the same

ABSTRACT

A low density parity check (LDPC) encoder, an LDPC decoder, and an LDPC encoding method are disclosed. The LDPC encoder includes first memory, second memory, and a processor. The first memory stores an LDPC codeword having a length of 16200 and a code rate of 3/15. The second memory is initialized to 0. The processor generates the LDPC codeword corresponding to information bits by performing accumulation with respect to the second memory using a sequence corresponding to a parity check matrix (PCM).

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims priority of U.S.application Ser. No. 15/272,142, filed Sep. 21, 2016, which is acontinuation of U.S. application Ser. No. 14/496,356, filed Sep. 25,2014, now U.S. Pat. No. 9,490,846, which claims the benefit of KoreanPatent Application Nos. 10-2014-0106174 and 10-2014-0120009, filed Aug.14, 2014 and Sep. 11, 2014, respectively, which are hereby incorporatedby reference herein in their entirety.

BACKGROUND 1. Technical Field

The present disclosure relates generally to a low density parity check(LDPC) code that is used to correct errors occurring over a wirelesschannel, and, more particularly, to an LDPC code that is applicable to adigital broadcasting system.

2. Description of the Related Art

Current terrestrial television (TV) broadcasting generates co-channelinterference across an area within a distance that is three times aservice radius, and thus the same frequency cannot be reused in the areawithin the distance that is three times the service radius. An area inwhich the same frequency cannot be reused is called a white space.Spectrum efficiency significantly deteriorates due to the occurrence ofa white space.

Accordingly, there arises a need for the development of a transmissiontechnology that facilitates the elimination of a white space and thereuse of a frequency with an emphasis on reception robustness in orderto improve spectrum efficiency.

In response to this, the paper “Cloud Transmission: A New Spectrum-ReuseFriendly Digital Terrestrial Broadcasting Transmission System” publishedon Sep. of 2012 in IEEE Transactions on Broadcasting, Vol. 58, No. 3proposes a terrestrial cloud transmission technology that facilitatesreuse, does not generate a white space, and makes the construction andoperation of a single frequency network easy.

Using this terrestrial cloud transmission technology, a broadcastingstation can transmit the same nationwide content or locally differentcontent over a single broadcasting channel. However, for this purpose, areceiver should receive one or more terrestrial cloud broadcast signalsin an area in which signals transmitted from different transmittersoverlap each other, that is, an overlap area, over a single frequencynetwork, and then should distinguish and demodulate the receivedterrestrial cloud broadcast signals. That is, the receiver shoulddemodulate one or more cloud broadcast signals in a situation in whichco-channel interference is present and the timing and frequencysynchronization between transmitted signals are not guaranteed.

Meanwhile, Korean Patent Application Publication No. 2013-0135746entitled “Low Density Parity Check Code for Terrestrial CloudTransmission” discloses an LDPC code that is optimized for terrestrialcloud transmission and exhibits excellent performance at low code rate(<0.5).

However, Korean Patent Application Publication No. 2013-0135746 isdirected to a code length completely different from an LDPC code lengthused in the DVB broadcast standard, etc., and does not teach a specificLDPC encoding method.

SUMMARY

At least one embodiment of the present invention is directed to theprovision of a new LDPC codeword having a length of 16200 and a coderate of 3/15, which is capable of being used for general purposes.

At least one embodiment of the present invention is directed to theprovision of an LDPC encoding technique that is capable of efficientlyperforming LDPC encoding using a sequence having a number of rows equalto a value that is obtained by dividing the sum of the length of thesystematic part of an LDPC codeword, that is, 3240, and the length ofthe first parity part of the LDPC codeword, that is, 1080, by 360.

In accordance with an aspect of the present invention, there is providedan LDPC encoder, including first memory configured to store an LDPCcodeword having a length of 16200 and a code rate of 3/15; second memoryconfigured to be initialized to 0; and a processor configured togenerate the LDPC codeword corresponding to information bits byperforming accumulation with respect to the second memory using asequence corresponding to a parity check matrix (PCM).

The accumulation may be performed at parity bit addresses that areupdated using the sequence corresponding to the PCM.

The LDPC codeword may include a systematic part corresponding to theinformation bits and having a length of 3240, a first parity partcorresponding to a dual diagonal matrix included in the PCM and having alength of 1080, and a second parity part corresponding to an identitymatrix included in the PCM and having a length of 11880.

The sequence may have a number of rows equal to the sum of a valueobtained by dividing a length of the systematic part, that is, 3240, bya circulant permutation matrix (CPM) size corresponding to the PCM, thatis, 360, and a value obtained by dividing a length of the first paritypart, that is, 1080, by the CPM size.

The sequence may be represented by the following Sequence Table:

Sequence Table 1st row: 8 372 841 4522 5253 7430 8542 9822 10550 1189611988 2nd row: 80 255 667 1511 3549 5239 5422 5497 7157 7854 11267 3rdrow: 257 406 792 2916 3072 3214 3638 4090 8175 8892 9003 4th row: 80 150346 1883 6838 7818 9482 10366 10514 11468 12341 5th row: 32 100 978 34936751 7787 8496 10170 10318 10451 12561 6th row: 504 803 856 2048 67757631 8110 8221 8371 9443 10990 7th row: 152 283 696 1164 4514 4649 72607370 11925 11986 12092 8th row: 127 1034 1044 1842 3184 3397 5931 757711898 12339 12689 9th row: 107 513 979 3934 4374 4658 7286 7809 883010804 10893 10th row: 2045 2499 7197 8887 9420 9922 10132 10540 1081611876 11st row: 2932 6241 7136 7835 8541 9403 9817 11679 12377 1281012nd row: 2211 2288 3937 4310 5952 6597 9692 10445 11064 11272

The accumulation may be performed while the rows of the sequence arebeing repeatedly changed by the CPM size of the PCM.

In accordance with an aspect of the present invention, there is providedan LDPC encoding method, including initializing first memory configuredto store an LDPC codeword having a length of 16200 and a code rate of3/15, and second memory; and generating the LDPC codeword correspondingto information bits by performing accumulation with respect to thesecond memory using a sequence corresponding to a PCM.

The accumulation may be performed at parity bit addresses that areupdated using the sequence corresponding to the PCM.

The LDPC codeword may include a systematic part corresponding to theinformation bits and having a length of 3240, a first parity partcorresponding to a dual diagonal matrix included in the PCM and having alength of 1080, and a second parity part corresponding to an identitymatrix included in the PCM and having a length of 11880.

The sequence may have a number of rows equal to the sum of a valueobtained by dividing a length of the systematic part, that is, 3240, bya circulant permutation matrix (CPM) size corresponding to the PCM, thatis, 360, and a value obtained by dividing a length of the first paritypart, that is, 1080, by the CPM size.

The sequence may be represented by the above Sequence Table.

In accordance with still another aspect of the present invention, thereis provided an LDPC decoder, including a receiving unit configured toreceive an LDPC codeword encoded using a sequence corresponding to a PCMand is represented by the above Sequence Table; and a decoding unitconfigured to restore information bits from the received LDPC codewordby performing decoding corresponding to the PCM.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will be more clearly understood from the following detaileddescription taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 is a block diagram illustrating a broadcast signal transmissionand reception system according to an embodiment of the presentinvention;

FIG. 2 is an operation flowchart illustrating a broadcast signaltransmission and reception method according to an embodiment of thepresent invention;

FIG. 3 is a diagram illustrating the structure of a PCM corresponding toan LDPC code to according to an embodiment of the present invention;

FIG. 4 is a block diagram illustrating an LDPC encoder according to anembodiment of the present invention:

FIG. 5 is a block diagram illustrating an LDPC decoder according to anembodiment of the present invention;

FIG. 6 is an operation flowchart illustrating an LDPC encoding methodaccording to an embodiment of the present invention; and

FIG. 7 is a graph plotting the performance of a QC-LDPC code having alength of 16200 and a code rate of 3/15 according to an embodiment ofthe present invention against E_(b)/N_(o).

DETAILED DESCRIPTION

Embodiments of the present invention will be described in detail belowwith reference to the accompanying drawings. Repeated descriptions anddescriptions of well-known functions and configurations that have beendeemed to make the gist of the present invention unnecessarily obscurewill be omitted below. The embodiments of the present invention areintended to fully describe the present invention to persons havingordinary knowledge in the art to which the present invention pertains.Accordingly, the shapes, sizes, etc. of components in the drawings maybe exaggerated to make the description obvious.

Embodiments of the present invention will be described in detail belowwith reference to the accompanying drawings.

FIG. 1 is a block diagram illustrating a broadcast signal transmissionand reception system according to an embodiment of the presentinvention.

Referring to FIG. 1, it can be seen that a transmitter 10 and a receiver30 communicate with each other over a wireless channel 20.

The transmitter 10 generates an n-bit codeword by encoding k informationbits using an LDPC encoder 13. The codeword is modulated by themodulator 15, and is transmitted via an antenna 17. The signaltransmitted via the wireless channel 20 is received via the antenna 31of the receiver 30, and, in the receiver 30, is subjected to a processreverse to the process in the transmitter 10. That is, the received datais demodulated by a demodulator 33, and is then decoded by an LDPCdecoder 35, thereby finally restoring the information bits.

It will be apparent to those skilled in the art that the above-describedtransmission and reception processes have been described within aminimum range required for a description of the features of the presentinvention and various processes required for data transmission may beadded.

In the following, the specific processes of encoding and decoding thatare performed using an LDPC code in the LDPC encoder 13 or LDPC decoder35 and the specific configurations of encoding and decoding devices,such as the LDPC encoder 13 and the LDPC decoder 35, are described. TheLDPC encoder 13 illustrated in FIG. 1 may have a structure illustratedin FIG. 4, and the LDPC decoder 35 may have a structure illustrated inFIG. 5.

FIG. 2 is an operation flowchart illustrating a broadcast signaltransmission and reception method according to an embodiment of thepresent invention.

Referring to FIG. 2, in the broadcast signal transmission and receptionmethod according to this embodiment of the present invention, input bits(information bits) are subjected to LDPC encoding at step S210.

That is, at step S210, an n-bit codeword is generated by encoding kinformation bits using the LDPC encoder.

In this case, step S210 may be performed as in an LDPC encoding methodillustrated in FIG. 6.

Furthermore, in the broadcast signal transmission and reception method,the encoded data is modulated at step S220.

That is, at step S220, the encoded n-bit codeword is modulated using themodulator.

Furthermore, in the broadcast signal transmission and reception method,the modulated data is transmitted at step S230.

That is, at step S230, the modulated codeword is transmitted over awireless channel via the antenna.

Furthermore, in the broadcast signal transmission and reception method,the received data is demodulated at step S240.

That is, at step S240, the signal transmitted over the wireless channelis received via the antenna of the receiver, and the received data isdemodulated using the demodulator.

Furthermore, in the broadcast signal transmission and reception method,the demodulated data is subjected to LDPC decoding at step S250.

That is, at step S250, the information bits are finally restored byperforming LDPC decoding using the demodulator of the receiver.

In this case, step S250 corresponds to a process reverse to that of theLDPC encoding method illustrated in FIG. 6, and may correspond to theLDPC decoder of FIG. 5.

An LDPC code is known as a code very close to the Shannon limit for anadditive white Gaussian noise (AWGN) channel, and has the advantages ofasymptotically excellent performance and parallelizable decodingcompared to a turbo code.

Generally, an LDPC code is defined by a low-density parity check matrix(PCM) that is randomly generated. However, a randomly generated LDPCcode requires a large amount of memory to store a PCM, and requires alot of time to access memory. In order to overcome these problems, aquasi-cyclic LDPC (QC-LDPC) code has been proposed. A QC-LDPC code thatis composed of a zero matrix or a circulant permutation matrix (CPM) isdefined by a PCM that is expressed by the following Equation 1:

$\begin{matrix}{{H = \begin{bmatrix}J^{a_{11}} & J^{a_{12}} & \ldots & J^{a_{1n}} \\J^{a_{21}} & J^{a_{22}} & \ldots & J^{a_{2n}} \\\vdots & \vdots & \ddots & \vdots \\J^{a_{m\; 1}} & J^{a_{m\; 2}} & \ldots & J^{a_{mn}}\end{bmatrix}},{{{for}\mspace{14mu} a_{ij}} \in \left\{ {0,1,\ldots \mspace{14mu},{L - 1},\infty} \right\}}} & (1)\end{matrix}$

In this equation, J is a CPM having a size of L×L , and is given as thefollowing Equation 2. In the following description, L may be 360.

$\begin{matrix}{J_{L \times L} = \begin{bmatrix}0 & 1 & 0 & \ldots & 0 \\0 & 0 & 1 & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots \\0 & 0 & 0 & \ldots & 1 \\1 & 0 & 0 & \ldots & 0\end{bmatrix}} & (2)\end{matrix}$

Furthermore, J′ is obtained by shifting an L×L identity matrix I (J⁰) tothe right i (0≤i<L) times, and J^(∞) is an L×L zero matrix. Accordingly,in the case of a QC-LDPC code, it is sufficient if only index exponent iis stored in order to store J^(i), and thus the amount of memoryrequired to store a PCM is considerably reduced.

FIG. 3 is a diagram illustrating the structure of a PCM corresponding toan LDPC code to according to an embodiment of the present invention.

Referring to FIG. 3, the sizes of matrices A and C are g×K and(N−K−g)×(K+g), respectively, and are composed of an L×L zero matrix anda CPM, respectively. Furthermore, matrix Z is a zero matrix having asize of g×(N−K−g), matrix D is an identity matrix having a size of(N−K−g)×(N−K−g), and matrix B is a dual diagonal matrix having a size ofg×g. In this case, the matrix B may be a matrix in which all elementsexcept elements along a diagonal line and neighboring elements below thediagonal line are 0, and may be defined as the following Equation 3:

$\begin{matrix}{B_{g \times g} = \begin{bmatrix}I_{L \times L} & 0 & 0 & \ldots & 0 & 0 & 0 \\I_{L \times L} & I_{L \times L} & 0 & \ldots & 0 & 0 & 0 \\0 & I_{L \times L} & I_{L \times L} & \vdots & 0 & 0 & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \\0 & 0 & 0 & \ldots & I_{L \times L} & I_{L \times L} & 0 \\0 & 0 & 0 & \ldots & 0 & I_{L \times L} & I_{L \times L}\end{bmatrix}} & (3)\end{matrix}$

where L_(L×L) is an identity matrix having a size of L×L.

That is, the matrix B may be a bit-wise dual diagonal matrix, or may bea block-wise dual diagonal matrix having identity matrices as itsblocks, as indicated by Equation 3. The bit-wise dual diagonal matrix isdisclosed in detail in Korean Patent Application Publication No.2007-0058438, etc.

In particular, it will be apparent to those skilled in the art that whenthe matrix B is a bit-wise dual diagonal matrix, it is possible toperform conversion into a Quasi-cyclic form by applying row or columnpermutation to a PCM including the matrix B and having a structureillustrated in FIG. 3.

In this case, N is the length of a codeword, and K is the length ofinformation.

The present invention proposes a newly designed QC-LDPC code in whichthe code rate thereof is 3/15 and the length of a codeword is 16200, asillustrated in the following Table 1. That is, the present inventionproposes an LDPC code that is designed to receive information having alength of 3240 and generate an LDPC codeword having a length of 16200.

Table 1 illustrates the sizes of the matrices A, B, C, D and Z of theQC-LDPC code according to the present invention:

TABLE 1 Sizes Code rate Length A B C D Z 3/15 16200 1080 × 1080 × 11880× 11880 × 1080 × 3240 1080 4320 11880 11880

The newly designed LDPC code may be represented in the form of asequence (progression), an equivalent relationship is establishedbetween the sequence and matrix (parity bit check matrix), and thesequence may be represented, as follows:

Sequence Table 1st row: 8 372 841 4522 5253 7430 8542 9822 10550 1189611988 2nd row: 80 255 667 1511 3549 5239 5422 5497 7157 7854 11267 3rdrow: 257 406 792 2916 3072 3214 3638 4090 8175 8892 9003 4th row: 80 150346 1883 6838 7818 9482 10366 10514 11468 12341 5th row: 32 100 978 34936751 7787 8496 10170 10318 10451 12561 6th row: 504 803 856 2048 67757631 8110 8221 8371 9443 10990 7th row: 152 283 696 1164 4514 4649 72607370 11925 11986 12092 8th row: 127 1034 1044 1842 3184 3397 5931 757711898 12339 12689 9th row: 107 513 979 3934 4374 4658 7286 7809 883010804 10893 10th row: 2045 2499 7197 8887 9420 9922 10132 10540 1081611876 11st row: 2932 6241 7136 7835 8541 9403 9817 11679 12377 1281012nd row: 2211 2288 3937 4310 5952 6597 9692 10445 11064 11272

An LDPC code that is represented in the form of a sequence is beingwidely used in the DVB standard.

According to an embodiment of the present invention, an LDPC codepresented in the form of a sequence is encoded, as follows. It isassumed that there is an information block S=(s₀, s₁, . . . , s_(K−1))having an information size K. The LDPC encoder generates a codewordΛ=(λ₀, λ₁, λ₂, . . . , λ_(N−1)) having a size of N=K+M₁+M₂ using theinformation block S having a size K. In this case, M₁=g, and M₂=N−K−g.Furthermore, M₁ size of parity bits corresponding to the dual diagonalmatrix B, and M₂ is the size of parity bits corresponding to theidentity matrix D. The encoding process is performed, as follows:

Initialization:

λ_(i) =s _(i) for i=0,1, . . . , K−1

p _(j)=0 for j=0,1, . . . , M ₁ +M ₂−1  (4)

First information bit λ₀ is accumulated at parity bit addressesspecified in the 1st row of the sequence of the Sequence Table. Forexample, in an LDPC code having a length of 16200 and a code rate of3/15, an accumulation process is as follows:

p₈=p₈⊕λ₀ p₃₇₂=p₃₇₂⊕λ₀ p₈₄₁=p₈₄₁⊕λ₀ p₄₅₂₂=p₄₅₂₂⊕λ₀ p₅₂₅₃=p₅₂₅₃⊕λ₀p₇₄₃₀=p₇₄₃₀⊕λ₀ p₈₅₄₂=p₈₅₄₂⊕λ₀ p₉₈₂₂=p₉₈₂₂⊕λ₀ p₁₀₅₅₀=p₁₀₅₅₀⊕λ₀p₁₁₈₉₆=p₁₁₈₉₆⊕λ₀ p₁₁₉₈₈=p₁₁₉₈₈⊕λ₀

where the addition ⊕ occurs in GF(2).

The subsequent L−1 information bits, that is, λ_(m), m=1,2, . . . , L−1,are accumulated at parity bit addresses that are calculated by thefollowing Equation 5:

(x+m×Q ₁)mod M ₁ if x<M ₁

M ₁+{(x−M ₁ +m×Q ₂)mod M ₂} if x≥M ₁  (5)

where x denotes the addresses of parity bits corresponding to the firstinformation bit λ₀, that is, the addresses of the parity bits specifiedin the first row of the sequence of the Sequence Table, Q₁=M₁/L,Q₂=M₂/L, and L=360. Furthermore, Q₁ and Q₂ are defined in the followingTable 2. For example, for an LDPC code having a length of 16200 and acode rate of 3/15, M₁=1080, Q₁=3, M₂=11880, Q₂=33 and L=360, and thefollowing operations are performed on the second bit λ₁ using Equation5:

p₁₁=p₁₁⊕λ₁ p₃₇₅=p₃₇₅⊕λ₁ p₈₄₄=p₈₄₄⊕λ₁ p₄₅₅₅=p₄₅₅₅⊕λ₁ p₅₂₈₆=p₅₂₈₆⊕λ₁p₇₄₆₃=p₇₄₆₃⊕λ₁ p₈₅₇₅=p₈₅₇₅⊕λ₁ p₉₈₅₅=p₉₈₅₅⊕λ₁ p₁₀₅₈₃=p₁₀₅₈₃⊕λ₁p₁₁₉₂₉=p₁₁₉₂₉⊕λ₁ p₁₂₀₂₁=p₁₂₀₂₁⊕λ₁

Table 2 illustrates the sizes of M₁, Q₁, M₂ and Q₂ of the designedQC-LDPC code:

TABLE 2 Sizes Code rate Length M₁ M₂ Q₁ Q₂ 3/15 16200 1080 11880 3 33

The addresses of parity bit accumulators for new 360 information bitsfrom λ_(L) to λ_(2L−1) are calculated and accumulated from Equation 5using the second row of the sequence.

In a similar manner, for all groups composed of new L information bits,the addresses of parity bit accumulators are calculated and accumulatedfrom Equation 5 using new rows of the sequence.

After all the information bits from λ₀ to λ_(K−1) have been exhausted,the operations of the following Equation 6 are sequentially performedfrom i=1:

p _(i) =p _(i) ⊕p _(i−1) for i=0,1, . . . , M ₁−1  (6)

Thereafter, when a parity interleaving operation, such as that of thefollowing Equation 7, is performed, parity bits corresponding to thedual diagonal matrix B are generated:

λ_(K+L·t+s) =p _(Q) ₁ _(·s+t) for 0≤s<L, 0≤t<Q ₁  (7)

When the parity bits corresponding to the dual diagonal matrix B havebeen generated using K information bits λ₀, λ₁, . . . , λ_(K−1), paritybits corresponding to the identity matrix D are generated using the M₁generated parity bits λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹.

For all groups composed of L information bits from λ_(K) to λ_(K+M) ₁⁻¹, the addresses of parity bit accumulators are calculated using thenew rows (starting with a row immediately subsequent to the last rowused when the parity bits corresponding to the dual diagonal matrix Bhave been generated) of the sequence and Equation 5, and relatedoperations are performed.

When a parity interleaving operation, such as that of the followingEquation 8, is performed after all the information bits from λ_(K) toλ_(K+M) ₁ ⁻¹, have been exhausted, parity bits corresponding to theidentity matrix D are generated:

λ_(K+M) ₁ _(+L·t+s) =p _(M) ₁ _(+Q) ₂ _(·s+t) for 0≤s<L, 0≤t<Q ₂  (8)

FIG. 4 is a block diagram illustrating an LDPC encoder according to anembodiment of the present invention.

Referring to FIG. 4, the LDPC encoder according to this embodiment ofthe present invention includes memory 310 and 320 and a processor 330.

The memory 310 is memory that is used to store an LDPC codeword having alength of 16200 and a code rate of 3/15.

The memory 320 is memory that is initialized to 0.

The memory 310 and the memory 320 may correspond to λ_(i) (i=0,1, . . ., N−1) and p_(j) (j=0,1, . . . , M₁+M₂−1), respectively.

The memory 310 and the memory 320 may correspond to various types ofhardware for storing sets of bits, and may correspond to datastructures, such as an array, a list, a stack and a queue.

The processor 330 generates an LDPC codeword corresponding toinformation bits by performing accumulation with respect to the memory320 using a sequence corresponding to a PCM.

In this case, the accumulation may be performed at parity bit addressesthat are updated using the sequence of the above Sequence Table.

In this case, the LDPC codeword may include a systematic part λ₀, λ₁, .. . , λ_(K−1) corresponding to the information bits and having a lengthof 3240 (=K), a first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹corresponding to a dual diagonal matrix included in the PCM and having alength of 1080 (=M₁=g), and a second parity part λ_(K+M) ₁ , λ_(K+M) ₁₊₁, . . . , λ_(K+M) ₁ _(+M) ₂ ⁻¹ corresponding to an identity matrixincluded in the PCM and having a length of 11880 (=M₂).

In this case, the sequence may have a number of rows equal to the sum(3240/360+1080/360=12) of a value obtained by dividing the length of thesystematic part, that is, 3240, by a CPM size L corresponding to thePCM, that is, 360, and a value obtained by dividing the length M₁ of thefirst parity part, that is, 1080, by 360.

As described above, the sequence may be represented by the aboveSequence Table.

In this case, the memory 320 may have a size corresponding to the sumM₁+M₂ of the length M₁ of the first parity part and the length M₂ of thesecond parity part.

In this case, the parity bit addresses may be updated based on theresults of comparing each x of the previous parity bit addressesspecified in respective rows of the sequence with the length M₁ of thefirst parity part.

That is, the parity bit addresses may be updated using Equation 5. Inthis case, x may be the previous parity bit addresses, m may be aninformation bit index that is an integer larger than 0 and smaller thanL, L may be the CPM size of the PCM, Q₁ may be M₁/L, M₁ may be the sizeof the first parity part, Q₂ may be M₂/L, and M₂ may be the size of thesecond parity part.

In this case, it may be possible to perform the accumulation whilerepeatedly changing the rows of the sequence by the CPM size L (=360) ofthe PCM, as described above.

In this case, the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹may be generated by performing parity interleaving using the memory 310and the memory 320, as described in conjunction with Equation 7.

In this case, the second parity part λ_(K+M) ₁ , λ_(K+M) ₁ ₊₁, . . . ,λ_(K+M) ₁ _(+M) ₂ ⁻¹ may be generated by performing parity interleavingusing the memory 310 and the memory 320 after generating the firstparity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹ and then performing theaccumulation using the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M)₁ ⁻¹ and the sequence, as described in conjunction with Equation 8.

FIG. 5 is a block diagram illustrating an LDPC decoder according to anembodiment of the present invention.

Referring to FIG. 5, the LDPC decoder according to this embodiment ofthe present invention may include a receiving unit 410 and a decodingunit 420.

The receiving unit 410 receives an LDPC codeword that has been encodedusing a sequence that corresponds to a PCM and is represented by theabove Sequence Table.

The decoding unit 420 restores information bits from the received LDPCcodeword by performing decoding corresponding to the PCM.

In this case, the sequence may be used to update the parity bitaddresses of the memory, and the parity bit addresses are used foraccumulation that is performed to generate parity bits corresponding tothe LDPC codeword.

In this case, the LDPC codeword may include a systematic part λ₀, λ₁, .. . , λ_(K−1) corresponding to the information bits, a first parity partλ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹ corresponding to a dual diagonalmatrix included in the PCM, and a second parity part λ_(K+M) ₁ , λ_(K+M)₁ ₊₁, . . . , λ_(K+M) ₁ _(+M) ₂ ⁻¹ corresponding to an identity matrixincluded in the PCM.

In this case, the parity bit addresses may be updated based on theresults of comparing each x of the previous parity bit addressesspecified in respective rows of the sequence with the length M₁ of thefirst parity part.

That is, the parity bit addresses may be updated using Equation 5. Inthis case, x may be the previous parity bit addresses, m may be aninformation bit index that is an integer larger than 0 and smaller thanL, L may be the CPM size of the PCM, Q₁ may be M₁/L, M₁ may be the sizeof the first parity part, Q₂ may be M₂/L, and M₂ may be the size of thesecond parity part.

FIG. 6 is an operation flowchart illustrating an LDPC encoding methodaccording to an embodiment of the present invention.

Referring to FIG. 6, the LDPC encoding method according to thisembodiment of the present invention initializes the first memory thatstores an LDPC codeword having a length of 16200 and a code rate of3/15, and second memory at step S510.

In this case, step S510 may be performed using Equation 4.

Furthermore, in the LDPC encoding method according to this embodiment ofthe present invention, an LDPC codeword corresponding to informationbits is generated by performing accumulation with respect to the secondmemory using a sequence corresponding to a PCM at step S520.

In this case, the accumulation may be performed at parity bit addressesthat are updated using the sequence corresponding to the PCM.

In this case, the LDPC codeword may include a systematic part λ₀, λ₁, .. . , λ_(K−1) corresponding to the information bits and having a lengthof 3240 (=K), a first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹corresponding to a dual diagonal matrix included in the PCM and having alength of 1080 (=M₁=g), and a second parity part λ_(K+M) ₁ , λ_(K+M) ₁₊₁, . . . , λ_(K+M) ₁ _(+M) ₂ ⁻¹ corresponding to an identity matrixincluded in the PCM and having a length of 11880 (=M₂).

In this case, the sequence may have a number of rows equal to the sum(3240/360+1080/360=12) of a value obtained by dividing the length of thesystematic part, that is, 3240, by a CPM size L corresponding to thePCM, that is, 360, and a value obtained by dividing the length M₁ of thefirst parity part, that is, 1080, by 360.

As described above, the sequence may be represented by the aboveSequence Table.

In this case, the parity bit addresses may be updated based on theresults of comparing each x of the previous parity bit addressesspecified in respective rows of the sequence with the length M₁ of thefirst parity part.

That is, the parity bit addresses may be updated using Equation 5. Inthis case, x may be the previous parity bit addresses, m may be aninformation bit index that is an integer larger than 0 and smaller thanL, L may be the CPM size of the PCM, Q₁ may be M₁/L, M, may be the sizeof the first parity part, Q₂ may be M₂/L, and M₂ may be the size of thesecond parity part.

In this case, it may be possible to perform the accumulation whilerepeatedly changing the rows of the sequence by the CPM size L (=360) ofthe PCM, as described above.

In this case, the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹may be generated by performing parity interleaving using the memory 310and the memory 320, as described in conjunction with Equation 7.

In this case, the second parity part λ_(K+M) ₁ , λ_(K+M) ₁ ₊₁, . . . ,λ_(K+M) ₁ _(+M) ₂ ⁻¹ may be generated by performing parity interleavingusing the memory 310 and the memory 320 after generating the firstparity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹ and then performing theaccumulation using the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M)₁ ₊₁ and the sequence, as described in conjunction with Equation 8.

FIG. 7 is a graph plotting the performance of a QC-LDPC code having alength of 16200 and a code rate of 3/15 according to an embodiment ofthe present invention against E_(b)/N_(o).

The graph illustrated in FIG. 7 illustrates results that were obtainedon the assumption that a log-likelihood ratio (LLR)-based sum-productalgorithm in which binary phase shift keying (BPSK) modulation and 50rounds of repetitive decoding were performed was used for computationalexperiments. As illustrated in FIG. 7, it can be seen that the designedcode is away from the Shannon limit by about 1.25 dB at BER=10⁻⁶.

At least one embodiment of the present invention has the advantage ofproviding a new LDPC codeword having a length of 16200 and a code rateof 3/15, which is capable of being used for general purposes.

At least one embodiment of the present invention has the advantage ofproviding an LDPC encoding technique that is capable of efficientlyperforming LDPC encoding using a sequence having a number of rows equalto a value that is obtained by dividing the sum of the length of thesystematic part of an LDPC codeword, that is, 3240, and the length ofthe first parity part of the LDPC codeword, that is, 1080, by 360.

Although the specific embodiments of the present invention have beendisclosed for illustrative purposes, those skilled in the art willappreciate that various modifications, additions and substitutions arepossible without departing from the scope and spirit of the invention asdisclosed in the accompanying claims.

What is claimed is:
 1. A low density parity check (LDPC) decoder,comprising: a receiving unit configured to receive a signalcorresponding to an LDPC codeword having a length of 16200 and a coderate of 3/15, the LDPC codeword encoded using a sequence correspondingto a parity check matrix (PCM); and a decoding unit configured toperform decoding the received signal, the decoding corresponding to theparity check matrix.
 2. The LDPC decoder of claim 1, wherein thesequence is represented by the following Sequence Table: Sequence Table1st row: 8 372 841 4522 5253 7430 8542 9822 10550 11896 11988 2nd row:80 255 667 1511 3549 5239 5422 5497 7157 7854 11267 3rd row: 257 406 7922916 3072 3214 3638 4090 8175 8892 9003 4th row: 80 150 346 1883 68387818 9482 10366 10514 11468 12341 5th row: 32 100 978 3493 6751 77878496 10170 10318 10451 12561 6th row: 504 803 856 2048 6775 7631 81108221 8371 9443 10990 7th row: 152 283 696 1164 4514 4649 7260 7370 1192511986 12092 8th row: 127 1034 1044 1842 3184 3397 5931 7577 11898 1233912689 9th row: 107 513 979 3934 4374 4658 7286 7809 8830 10804 1089310th row: 2045 2499 7197 8887 9420 9922 10132 10540 10816 11876 11strow: 2932 6241 7136 7835 8541 9403 9817 11679 12377 12810 12nd row: 22112288 3937 4310 5952 6597 9692 10445 11064 11272


3. The LDPC decoder of claim 2, wherein the LDPC codeword comprises asystematic part corresponding to the information bits and having alength of 3240, a first parity part corresponding to a dual diagonalmatrix included in the PCM and having a length of 1080, and a secondparity part corresponding to an identity matrix included in the PCM andhaving a length of
 11880. 4. The LDPC decoder of claim 3, wherein thesequence has a number of rows equal to a sum of a value obtained bydividing a length of the systematic part, that is, 3240, by a circulantpermutation matrix (CPM) size corresponding to the PCM, that is, 360,and a value obtained by dividing a length of the first parity part, thatis, 1080, by the CPM size.
 5. The LDPC decoder of claim 2, wherein theLDPC codeword is generated by performing accumulation with respect to amemory and the accumulation is performed at parity bit addresses thatare updated using the sequence.
 6. The LDPC decoder of claim 5, whereinthe accumulation is performed while the rows of the sequence are beingrepeatedly changed by the CPM size of the PCM.
 7. A low density paritycheck (LDPC) decoding method, comprising: receiving a signalcorresponding to an LDPC codeword having a length of 16200 and a coderate of 3/15, the LDPC codeword encoded using a sequence correspondingto a parity check matrix (PCM); and decoding the received signal, thedecoding corresponding to the parity check matrix.